Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#4489 | C2 | semidirect |
| 5. C3×#64710 | C2 | semidirect |
| 6. #11745944 | C2 | semidirect |
| 7. #11745939 | C2 | semidirect |
| 20. #90936 | C4 | semidirect |
| 27. #64710 | D3 | semidirect |
| 42. C3×#672 | C2×C4 | semidirect |
| 43. C5×C3⋊C16 | C2×C4 | semidirect |
| 50. #4489 | D5 | semidirect |
| 103. #672 | C4×D3 | semidirect |
| 136. C3⋊C16 | C4×D5 | semidirect |
| 205. C3×C5 | #2159 | semidirect |
| 238. C5 | #69346 | semidirect |
| 250. C3 | #10600119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D15×#107 | 2 |
| #11747690 | 2 |
| C2×#90936 | 2 |
| C5×#4489 | 2 |
| C3×#64710 | 2 |
| #11745944 | 2 |
| #11745939 | 2 |
| #10600119 | 3 |
| #69346 | 5 |